library(plotly)
# Create a list of values for n
nlist <- c(seq(10, 200, 5))

# We simulate using the Gamma distribution
gammadf <- data.frame(nlist, unlist(lapply(nlist, function(x) pgamma(q = 1,shape=30,rate=x*.25))))
names(gammadf) <- c("n", "Probability")

# We simulate using the Poisson 
poisdf <- data.frame(nlist, unlist(lapply(nlist, function(x) qpois(0.95,x*.25*1,lower=F))))
names(poisdf) <- c("n", "Failures")
#poisdf
#gammadf
figGAMMA <- plot_ly(data = gammadf, x = ~n, y = ~Probability) %>% layout(title = "Estimating Probability of At Least 30 Failures with Gamma Distribution") 
#fig <- fig %>% add_trace(x = nlist[gammadf[,2] > 0.95][1], y =gammadf[,2][gammadf[,2] > 0.95][1])
figGAMMA
figPOIS <- plot_ly(data = poisdf, x = ~n, y = ~Failures) %>% layout(title = "Estimating At Least 30 Failures with Poission Distribution") 
figPOIS

We can see that from both figures, that a sample size of 160 is the optimal choice for having a 95% chance of at least 30 failures. We can see that the Poisson distribution has a very linear relationship between sample size and the amount of failed disks. Meanwhile, the gamma distribution’s relationship between sample size and probability of at least 30 failures has a much more